On Hamel bases in Banach spaces

Juan Carlos Ferrando. "On Hamel bases in Banach spaces." Studia Mathematica 220.2 (2014): 169-178. <http://eudml.org/doc/285478>.

@article{JuanCarlosFerrando2014,
abstract = {It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.},
author = {Juan Carlos Ferrando},
journal = {Studia Mathematica},
keywords = {Hamel basis; Banach space; -analytic space; countably - determined space; barrelled space},
language = {eng},
number = {2},
pages = {169-178},
title = {On Hamel bases in Banach spaces},
url = {http://eudml.org/doc/285478},
volume = {220},
year = {2014},
}

TY - JOUR
AU - Juan Carlos Ferrando
TI - On Hamel bases in Banach spaces
JO - Studia Mathematica
PY - 2014
VL - 220
IS - 2
SP - 169
EP - 178
AB - It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.
LA - eng
KW - Hamel basis; Banach space; -analytic space; countably - determined space; barrelled space
UR - http://eudml.org/doc/285478
ER -